相关论文: Non-spherical minimizers in the generalized liquid…

We consider the minimization problem of the functional given by the sum of the fractional perimeter and a general Riesz potential, which is one generalization of Gamow's liquid drop model. We first show the existence of minimizers for any…

This paper is concerned with volume-constrained minimization problems derived from Gamow's liquid drop model for the atomic nucleus, involving the competition of a perimeter term and repulsive nonlocal potentials. We consider a large class…

We consider a version of Gamow's liquid drop model with a short range attractive perimeter-penalizing potential and a long-range Coulomb interaction of a uniformly charged mass in $\R^3$. Here we constrain ourselves to minimizing among the…

We consider a variant of Gamow's liquid drop model, with a general repulsive Riesz kernel and a long-range attractive background potential with weight $Z$. The addition of the background potential acts as a regularization for the liquid…

We study a large family of axisymmetric Riesz-type singular interaction potentials with anisotropy in three dimensions. We generalize some of the results of our recent work in two dimensions to the present setting. For potentials with…

We revisit the liquid drop model with a general Riesz potential. Our new result is the existence of minimizers for the conjectured optimal range of parameters. We also prove a conditional uniqueness of minimizers and a nonexistence result…

The ancient Gamow liquid drop model of nuclear energies has had a renewed life as an interesting problem in the calculus of variations: Find a set $\Omega \subset \mathbb R^3$ with given volume A that minimizes the sum of its surface area…

We consider a variant of Gamow's liquid drop model with an anisotropic surface energy. Under suitable regularity and ellipticity assumptions on the surface tension, Wulff shapes are minimizers in this problem if and only if the surface…

In cluster physics a single particle potential to determine the microscopic part of the total energy of a collective configuration is necessary to calculate the shell- and pairing effects. In this paper we investigate the properties of the…

This paper is concerned with the macroscopic behavior of global energy minimizers in the three-dimensional sharp interface unscreened Ohta-Kawasaki model of diblock copolymer melts. This model is also referred to as the nuclear liquid drop…

Motivated by a number of realizations of long-range interacting systems, including ultra-cold atomic and molecular gases, we study a neutral plasma with power-law interactions longer-ranged than Coulombic. We find that beyond a crossover…

Motivated by Gamow's liquid drop model in the large mass regime, we consider an isoperimetric problem in which the standard perimeter $P(E)$ is replaced by $P(E)-\gamma P_\varepsilon(E)$, with $0<\gamma<1$ and $P_\varepsilon$ a nonlocal…

We introduce and study certain variants of Gamow's liquid drop model in which an anisotropic surface energy replaces the perimeter. After existence and nonexistence results are established, the shape of minimizers is analyzed. Under…

We establish the behavior of the energy of minimizers of non-local Ginzburg-Landau energies with Coulomb repulsion in two space dimensions near the onset of multi-droplet patterns. Under suitable scaling of the background charge density…

This is the first in a series of two papers in which we derive a $\Gamma$-expansion for a two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion, also known as the Ohta-Kawasaki model in connection with diblock copolymer…

We study a large family of Riesz-type singular interaction potentials with anisotropy in two dimensions. Their associated global energy minimizers are given by explicit formulas whose supports are determined by ellipses under certain…

We study a variational problem modeling the behavior at equilibrium of charged liquid drops under convexity constraint. After proving well-posedness of the model, we show C 1,1-regularity of minimizers for the Coulombic interaction in…

We study the gas-liquid phase diagram and the crossover behavior of a simple model of ionic fluid: an equimolar binary mixture of equisized hard spheres interacting through screened Coulomb potentials which are repulsive between particles…

In this paper we study pattern formation for a physical local/nonlocal interaction functional where the local attractive term is given by the $1$-perimeter and the nonlocal repulsive term is the Yukawa (or screened Coulomb) potential. This…

We establish the mean-field convergence for systems of points evolving along the gradient flow of their interaction energy when the interaction is the Coulomb potential or a super-coulombic Riesz potential, for the first time in arbitrary…